IF ONLY intuition could get us where we want to go. In the late 1960s, John Coltrane drew a mandala that connected five musical notes in patterns, including a five-pointed star. Inspired by Einstein’s work to unify physics in a single theory, the jazz musician’s diagram was an attempt to understand the connections between musical scales. Its form is so beautiful that it is tempting to wonder if there is a link between music and physics stretching all the way to a theory of everything.

That is unlikely, however. In his marvellous The Jazz of Physics, physicist and musician Stephon Alexander explains that analogies can seed new insights, but are no substitute for deep understanding of the thing itself. An intuitive analogy between music and physics is “part of the journey”, Alexander says, but during this long journey, the scenery will change. Not having an adequate analogy – and needing the clarity of rigorous calculations – is also part of the journey.

Ultimately, a physicist’s universe is mathematical: you can’t get at it through intuition alone. Mathematics, Alexander notes, “is like a new sense, beyond our physical senses, that enables us to comprehend things that we cannot understand solely through our… perceptions or intuitions”.

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It is a theme repeated in the extraordinary Bananaworld, in which Jeffrey Bub employs an innovative way of explaining the intricacies of quantum physics. He takes the state of a banana (peeled or unpeeled) and its flavour (ordinary or intense) as a more intuitive analogy for the state and quantum properties of particles. But Bub, too, is forced to lament intuition’s shortcomings: wave descriptions in quantum theory are “intuitively appealing”, but that appeal is “misleading”.

At school, we learn of electrons orbiting atoms, following Niels Bohr’s model, and we talk about fitting a certain number of whole waves into that orbital path, which gives us quantum structure. This is, however, an entirely erroneous way to think. The wave associated with a quantum system “evolves in an abstract, multidimensional representation space, not real physical space”, Bub points out. As Schrödinger said, using a wave to talk of quantum reality is “merely an adequate mathematical description of what happens”.

Despair, non-experts: it will always come back to the maths. “Mathematics is the light that illuminates physics, and mathematics-free physics has marked similarities to alcohol-free wine,” says Joseph Conlon in Why String Theory? This is why he says that his book, written for a lay audience, inevitably contains “only a shadow of the argument I would like to make”.

“Physicists must show they can recalibrate their ideas, or non-experts may spend taxes on other things”

Conlon delivers his argument, diluted as it is, with panache and humour. Chapter seven is only nine words long: “There is no direct experimental evidence for string theory.” And a section called “The world is described by quantum mechanics” is followed by a section called “The world really, honestly, truly is described by quantum mechanics.”

Conlon recognises why string theory is so controversial: many smart people are justifiably frustrated by the dislocation from testable reality, he says. His response is that, for all their good faith, most sceptics simply can’t appreciate what maths brings to the table. “The greater the ability to calculate in theoretical physics, the clearer the appeal of string theory becomes,” he says. “Nature really is written in the language of mathematics, and many results that flow easily using it are hard to justify in any other way.”

The lack of experimentation can cause string theory to be derided as “merely philosophy”. But we should be cautious about the subtext of such an accusation. Bub is a philosopher of physics, and the subject has never been more in need of input such as his: thoughtful, humble, informative. This is why, for me, Bananaworld should be mandatory reading for anyone studying or working in quantum or theoretical physics.

We live in dangerous times for theoretical physics. Experiments cannot distinguish between interpretations of quantum theory, verify which of the “final” theories is correct, or check the assumptions used to create cosmology’s narrative of our universe’s history.

Self-regulation and self-awareness are now vital. Perhaps theoretical physicists would benefit from philosophy retreats, where they could recalibrate their thinking and shed the pride and prejudice acquired in partisan departments. It is important that they show they can, otherwise the intuition of non-experts may lead them to spend taxes on things that feel more comfortable.

Even more important is that philosophy (and history) can fuel new ideas. Viewing theoretical physics and mathematics through other lenses may help us make headway. How else to grasp how primitive our understanding of reality really is? These books make it clear: for all our mathematical dexterity, in physics nobody knows anything. Yet.